Measurement of D⁰-D⁰ mixing and search for CP violation with D⁰ K^+^- decays

A measurement of the time-dependent ratio of the D⁰ K^+^- to D⁰ K^+^- decay rates is reported. The analysis uses a sample of proton-proton collisions corresponding to an integrated luminosity of 6 fb^-1 recorded by the LHCb experiment from 2015 through 2018 at a center-of-mass energy of 13 TeV. The D⁰ meson is required to originate from a D^*+ D⁰^+ decay, such that its flavor at production is inferred from the charge of the accompanying pion. The measurement is performed simultaneously for the K^+^- and K^-^+ final states, allowing both mixing and CP-violation parameters to be determined. The value of the ratio of the decay rates at production is determined to be R₊ = (343. 1 2. 0) 10^-5. The mixing parameters are measured to be c₊ = (51. 4 3. 5) 10^-4 and c₊^ = (13 4) 10^-6, where R₊c₊ is the linear coefficient of the expansion of the ratio as a function of decay time in units of the D⁰ lifetime, and c₊^ is the quadratic coefficient, both averaged between the K^+^- and K^-^+ final states. The precision is improved relative to the previous best measurement by approximately 60%. No evidence for CP violation is found.